More Dominoes

As with the earlier problem "Domino Magic Square", this problem
also asks for a magic square. From a regular set of dominoes,
remove all blanks, leaving 1-1, 1-2, ..., 6-6, 21 dominoes in all.
Remove three dominoes of your choice and arrange the remaining
18 dominoes in a 6x6 grid, such that the sum of the dots in
each row, column, and major diagonal is the same.

For example, removing the 6-6, 5-6, and either of 4-6, 5-5, will
result in each sum being 19. Removing 1-1, 1-2, and either of
1-3, 2-2, the sum must be 23. (Feel free to prove this.)

I usually do not post problems to which I have no solution, but
I have made an exception here. I came within 2 dominoes of a
solution, so I feel that one must exist. Please send whatever
solutions you have. As always, I will post any unique solutions and credit
the solver.